LONDON (Reuters) - The dollar fell on Tuesday and share markets flinched as news broke that U.S. President Donald Trump had ousted yet another of his top team, this time Secretary of State Rex Tillerson.

Trump said on Twitter he was replacing the former oil executive Tillerson with Mike Pompeo, the director of the Central Intelligence Agency(CIA), and that Gina Haspel would take over from Pompeo.

The announcement saw the dollar index, which measures the greenback against six other top world currencies, fall to a three-day low and meant the S&P 500 opened more subdued than traders had earlier expected.

"What we are seeing here is that those people in the U.S. administration in the more moderate line of thinking are being ousted, so this adds to the concerns the more radical forces are gaining some ground here," said Rabobank's Head of Macro Strategy Elwin de Groot.

The U.S. 10-year Treasury yield fell as much as 3 basis points on the Tillerson news and was last trading at around 2.84 percent , also held down by news of slowing inflation.

The MSCI All-Country World index of stocks, which tracks shares in 47 countries was less than 0.1 percent higher by 1305 GMT, with European stocks a fraction lower having started modestly higher.

The world index has recovered about half its losses sustained during a shakeout in stocks in February. The selloff came on the back of strong U.S. wage numbers, which investors feared might feed into inflation and push the U.S. central bank towards a faster pace of monetary tightening.

Raising its global growth forecasts, the Organisation for Economic Cooperation and Development (OECD) said the Fed would probably have to raise interest rates four times this year as inflation picks up.

Fed funds futures however, show markets pricing in a total of three rate hikes this year.

"We had a CPI (consumer price index) which was in line with expectations, which helped the stock market – investors were gearing themselves up for a stronger than consensus figure," said Investec economist Philip Shaw.

"Subsequently, that and Treasuries have reversed, that's on the fear that Tillerson's alleged removal will give the nationalists greater power within the White House over the globalists."

The pan-European STOXX 600 was last down 0.2 percent. Earlier in Asia though, MSCI's broadest regional index excluding Japan ended up 0.2 percent after spending much of the day struggling for direction.

In currencies, the dollar's dip on the Tillerson news was mainly against the euro. The Japanese yen was still half a percent down and at a two-week low, pressured by a political scandal engulfing Japanese Prime Minister Shinzo Abe's government.

Britain's pound rose to a one-week high. British finance minister Philip Hammond said in a mid-term budget update that the economy would grow slightly more quickly than previously expected and lowered the government's expected borrowing.

"We did have confirmation that public finances are better than expected and that there will be scope for spending increases in future years," said Sarah Hewin, head of research at Standard Chartered.

In commodities U.S. crude futures and Brent were both down half a percent each at 61.01 per barrel and 64.60 per barrel respectively.

Gold meanwhile bounced back into positive territory after the Tillerson news and after the U.S. inflation data.

(Reporting by Ritvik Carvalho; additional reporting by Saikat Chatterjee in LONDON and Asia markets team; Editing by Jon Boyle)